TR32 time series comparison Victor Venema. Content Jan Schween –Wind game: measurement and...
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Transcript of TR32 time series comparison Victor Venema. Content Jan Schween –Wind game: measurement and...
TR32 time series comparison
Victor Venema
Content
Jan Schween– Wind game: measurement and synthetic– Temporal resolution of 0.1 seconds
Heye Bogena– Wind, air pressure, water temperature– Temporal resolution of 10 minutes– Rollesbroich
Global Runoff Data Centre– Runoff Rhine Cologne– Daily, years: 1817 to 2001
Wind - Measurement and synthetic
Wind - distribution – normal plot
Increment distribution
Measurement: (t) Increment time series for lag l:
(x,l) = (t+l) - (t)
Distribution jumps sizes Width of the distribution is the mean variance at
scale l
Wind - Increment distribution
Daubechies wavelet family
Wind - Daubechies wavelet (db6)
Wind – Haar vs. Daubechies (db6)
Intermittency / Intermittence
On-off intermittency– Rain, eddy in laminar flow
Operationalisation: variance of variance (at a certain scale)
Intermittence is typically strongest at small scales
Time series modelling: Autoregressive conditional heteroskedasticity (ARCH, GARCH)
Multi-fractal models (not all)
Wind - Increment distribution
Structure functions
Increment time series: (x,l)=(t+l)- (t)
SF(l,q) = (1/N) Σ ||q
SF(l,2) is equivalent to auto-correlation function Correlated time series SF increases with l Higher q focuses on larger jumps For large l, SF equivalent to the moments
Wind – Structure functions
Fourier decomposition Decompose a time domain signal in sinuses of varying
wavelength Wavelength -> scale Fourier coefficients -> variance as function of scale
Wind – power spectrum
Wind speed (Heye Bogena; 10 min.)
Wavelet - Wind speed (10 min.)
Air pressure (10 min.)
Air pressure (10 min.) - Wavelets
Water temperature
Water temperature - Wavelets
Discharge all data and zoom
400 600 800 1000 1200 1400 1600 18000
5
10
Time (pixel)
Va
lue p-model
1894 1894.5 1895 1895.5 1896 1896.5 1897 1897.50
20
Time (year)
Ra
in (
mm
/d)
daily rain sums
1828 1828.5 1829 1829.5 1830 1830.5 1831 1831.5
500100015002000
Time (year)
Ru
no
ff (m
3/s
)
runoff Burghausen
1818 1818.5 1819 1819.5 1820 1820.5 1821 1821.5
2000400060008000
Time (year)
Ru
no
ff (m
3/s
)
runoff Cologne
0 200 400 600 800 1000 1200 1400 16000
0.2
0.4
Time (s)
LW
C (
g m
-3)
cumulus
0 200 400 600 800 1000
0.4
0.6
Time (s)
LW
C (
g m
-3)
stratocumulus
1894 1894.5 1895 1895.5 1896 1896.5 1897 1897.5-10
01020
Time (year)
Te
mp
. (°C
)
temperature
Discharge Rhine - Wavelets
Discharge Rhine
Discharge Rhine
Slope power spectrum vs. smoothness
Conclusions
Some signals showed annual, diurnal cycle Except for this no frequency was special
– Variability on all scales– Large scales:
white noise or even correlated variance is never gone
All signals showed intermittence– Typical for complex systems